be disconnected before applying charge to the remaining two. If, for example, LED5 was intended to be lit, X1 must be charged and X3 must be grounded. However, if X2 is also charged, LED3 would illuminate as well. If X2 was instead grounded, LED1 would illuminate, meaning that LED5 cannot be lit by itself. This can be solved by utilizing the tri-state logic properties of microcontroller pins. Microcontroller pins generally have three states: "high" (5 V), "low" (0 V) and "input". Input mode puts the pin into a high-impedance state, which, electrically speaking, "disconnects" that pin from the circuit, meaning little or no current will flow through it. This allows the circuit to see any number of pins connected at any time, simply by changing the state of the pin. In order to drive the six-LED matrix above, the two pins corresponding to the LED to be lit are connected to 5 V (I/O pin "high" = binary number 1) and 0 V (I/O pin "low" = binary 0), while the third pin is set in its input state. In doing so, current leakage out of the third pin is prevented, ensuring that the LED wished to be lit is the only one lit. Because the desired LED reduces the voltage available after the resistor, current will not flow across alternate paths (an alternate 2-LED path exists for every pair of pins in the 3-pin diagram, for example), so long as the voltage drop in the desired LED path is less than the total voltage drop across each string of alternative LEDs. However, in the variant with individual resistors this voltage-regulating effect does not affect the alternative paths so you must ensure that all LEDs used will not light with half the supply voltage applied because this variant does not benefit from the voltage-regulating effect of the desired path LED. By using tri-state logic, the matrix can theoretically be expanded to any size, as long as pins are available. For n pins, n(n − 1) LEDs can be in the matrix. Any LED can be lit by applying 5 V and 0 V to its corresponding pins and setting all of the other pins connected to the matrix to input mode. Under the same constraints as discussed above up to n − 1 LEDs sharing a common positive or negative path can be lit in parallel. Expanding The 3-wire circuit